
Computing Boundary Cycle of a PseudoTriangle Polygon from its Visibility Graph
Visibility graph of a simple polygon is a graph with the same vertex set...
read it

Terrain Visibility Graphs and Cyclic Polytope Triangulations
We prove a bijection between the triangulations of the 3dimensional cyc...
read it

Correct, Fast Remote Persistence
Persistence of updates to remote byteaddressable persistent memory (PM)...
read it

A mixture of experts model for predicting persistent weather patterns
Weather and atmospheric patterns are often persistent. The simplest weat...
read it

PseudoTriangle Visibility Graph: Characterization and Reconstruction
The visibility graph of a simple polygon represents visibility relations...
read it

Colouring polygon visibility graphs and their generalizations
Curve pseudovisibility graphs generalize polygon and pseudopolygon vis...
read it

Persistent Homology of Weighted Visibility Graph from Fractional Gaussian Noise
In this paper, we utilize persistent homology technique to examine the t...
read it
Terrain Visibility Graphs: Persistence is Not Enough
In this paper, we consider the Visibility Graph Recognition and Reconstruction problems in the context of terrains. Here, we are given a graph G with labeled vertices v_0, v_1, …, v_n1 such that the labeling corresponds with a Hamiltonian path H. G also may contain other edges. We are interested in determining if there is a terrain T with vertices p_0, p_1, …, p_n1 such that G is the visibility graph of T and the boundary of T corresponds with H. G is said to be persistent if and only if it satisfies the socalled Xproperty and Barproperty. It is known that every "pseudoterrain" has a persistent visibility graph and that every persistent graph is the visibility graph for some pseudoterrain. The connection is not as clear for (geometric) terrains. It is known that the visibility graph of any terrain T is persistent, but it has been unclear whether every persistent graph G has a terrain T such that G is the visibility graph of T. There actually have been several papers that claim this to be the case (although no formal proof has ever been published), and recent works made steps towards building a terrain reconstruction algorithm for any persistent graph. In this paper, we show that there exists a persistent graph G that is not the visibility graph for any terrain T. This means persistence is not enough by itself to characterize the visibility graphs of terrains, and implies that pseudoterrains are not stretchable.
READ FULL TEXT
Comments
There are no comments yet.